Clean up unused providers for AdvancedPaste (#43433)

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## Summary of the Pull Request
Clean up unused providers for AdvancedPaste

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## PR Checklist

- [x] Closes: #43429
- [ ] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [ ] **Tests:** Added/updated and all pass
- [ ] **Localization:** All end-user-facing strings can be localized
- [ ] **Dev docs:** Added/updated
- [ ] **New binaries:** Added on the required places
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- [ ] [WXS for
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- [ ] **Documentation updated:** If checked, please file a pull request
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## Detailed Description of the Pull Request / Additional comments

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src/settings-ui/Settings.UI/SettingsXAML/Views/AdvancedPastePage.xaml.cs

@@ -317,7 +317,6 @@ namespace Microsoft.PowerToys.Settings.UI.Views
             bool requiresEndpoint = serviceKind is AIServiceType.AzureOpenAI
                 or AIServiceType.AzureAIInference
                 or AIServiceType.Mistral
-                or AIServiceType.HuggingFace
                 or AIServiceType.Ollama;
             bool requiresDeployment = serviceKind == AIServiceType.AzureOpenAI;
             bool requiresApiVersion = serviceKind == AIServiceType.AzureOpenAI;
@@ -874,7 +873,6 @@ namespace Microsoft.PowerToys.Settings.UI.Views
                 AIServiceType.AzureOpenAI => "https://your-resource.openai.azure.com/",
                 AIServiceType.AzureAIInference => "https://{resource-name}.cognitiveservices.azure.com/",
                 AIServiceType.Mistral => "https://api.mistral.ai/v1/",
-                AIServiceType.HuggingFace => "https://api-inference.huggingface.co/models/",
                 AIServiceType.Ollama => "http://localhost:11434/",
                 _ => "https://your-resource.openai.azure.com/",
             };